Stability of linear time-invariant systems, such as low noise amplifiers (LNAs) or intermediate frequency amplifiers (IFAMPS), just to name two examples, can be a serious issue when large linearity is required and, therefore, both loop gain and bandwidth are high. The reason for this is that high linearity and large bandwidth normally only can be achieved by very high loop gain in combination with feedback. In order to achieve a large loop gain, in most applications, a large, uneven number of inverting stages are used to get negative feedback. However, stability problems occur when the phase of the loop-transfer function, in combination with unity loop-gain, becomes 180°.
FIG. 1 shows a simplified schematic of a feedback amplifier 100. The function for the closed-loop gain Acl of this amplifier can be defined by the following Equation 1.Out/In=Acl=d*A/1+A*k,  (Equation 1)where the closed-loop gain Acl approaches infinity when the (open) loop-gain Ak, becomes −1, i.e., when the phase of the loop-gain Ak is 180° at unity loop-gain. Therefore, traditional amplifiers are designed with a certain phase margin, which is the margin of the phase that is left at unity gain. There are several ways to design an amplifier with sufficient phase margin. In pole splitting, for example, the intrinsic phase transfer is modified in such a way that at unity gain the phase has enough margin with respect to the aforementioned 180°.
FIG. 2 shows an example of modification of the transfer function represented the amplitude characteristics |A|=|Vout/Iin| and phase characteristics φ=arctan(Vout/Iin), by adding pole-split components; in FIG. 2, a series circuit of a resistor R and a capacitor C are depicted as an example for pole-splitting components, which define the feedback function or factor k. However supply, process, and temperature variations often result in a different transfer function of the amplifier. A compensated amplifier not operating under nominal operating conditions always introduces a tradeoff with respect to linearity and bandwidth.
U.S. Pat. No. 6,232,834 discloses calibration of an integrated operational amplifier for optimization of the phase margin. The calibration is done to correct changes caused by operating temperature and supply voltages as well as process variations and aging that can affect the stability of the amplifier. A calibration circuit measures the response of the operational amplifier to a pulse input and controls a feedback impedance to produce an optimized phase margin. The output response to the pulse input is measured at two different times, at a first time close to the transition, capturing the peak overshoot from an underdamped amplifier and, at a second time, later than the first measurement when the distortions from the underdamped ringing have diminished. A quantizer circuit compares the two measured voltages and provides an input to control logic, which selects the amount of reactance in the feedback of the operational amplifier. The calibration terminates when the dampening of the amplifier has reached the least significant bit of adjustment available to the calibration process. However, U.S. Pat. No. 6,232,834 does not provide how the response of circuits operated at high frequencies can be measured.
At this moment, very robust design methods are used in order to make sure that radio frequency (RF) circuits perform under all conditions. This means that often circuits don't perform optimally because possible mismatches dictate less than optimal bias conditions. Accordingly, designing an amplifier in a traditional way often means that one needs to take into account numerous possibilities in which the circuit might be situated. For stability, a rule of thumb is a phase margin of 60° in nominal condition. Overall, this will lead to an amplifier that will be stable during worst-case situations.